A complete high precision set of deuteron analyzing powers for elastic deuteron- proton (dp) scattering at 250 MeV/nucleon (MeV/N) has been measured. The new data are presented together with data from previous measurements at 70, 100, 135 and 200 MeV/N. They are compared with the results of three- nucleon (3N) Faddeev calculations based on modern nucleon- nucleon (NN) potentials alone or combined with two models of three nucleon forces (3NFs): the Tucson-Melbourne 99 (TM99) and Urbana IX. At 250 MeV/N large discrepancies between pure NN models and data, which are not resolved by including 3NFs, were found at c. m. backward angles of theta(c.m). greater than or similar to 120 degrees for almost all the deuteron analyzing powers. These discrepancies are quite similar to those found for the cross section at the same energy. We found small relativistic effects that cannot resolve the discrepancies with the data indicating that other, short- ranged 3NFs are required to obtain a proper description of the data.